Osmosis and Osmotic Pressure: Deriving Van't Hoff's Law

This lecture discusses the concept of osmosis and osmotic pressure, focusing on their significance in biological systems. The instructor begins by explaining the nature of semi-permeable membranes and how they selectively allow certain molecules to pass. A system is described with two compartments separated by such a membrane, illustrating how a solution of salt and water behaves differently than pure water. The lecture details the equilibrium state of the system, where the chemical potentials of the solvent equalize across the membrane, while the solute remains confined. The instructor derives the relationship between osmotic pressure and the concentration of solute, leading to the formulation of Van't Hoff's law. This law quantitatively describes how osmotic pressure can be calculated based on the concentration of solute and temperature. The lecture concludes by summarizing the final expression for osmotic pressure, emphasizing its practical applications in understanding biological processes and solutions.